The use of fitted higher-order polynomial coefficients as covariates in the analysis of growth curves.

For orthogonal polynomials fitted to repeated measurements, a computer simulation study is used to investigate the effect of selecting higher-order coefficients as covariates in order to minimise the estimated variance of lower-order coefficients. Under the assumption that the repeated measurements have certain autoregressive covariance structures, it is seen that the gain in precision due to covariance adjustment can be largely illusory and that the resulting estimates of variances can grossly underestimate the true variances. The consequences of using all higher-order coefficients as covariates is also examined and seen to produce a gain in precision in certain circumstances.